Question11] $x^{2}+28 x-60$ 12] $x^{2}+7 x-30$

Studdy Solution

STEP 1

1. The problems involve factoring quadratic expressions.
2. Each quadratic is in the form $ax^2 + bx + c$ .
3. The goal is to factor each quadratic expression into two binomials.

STEP 2

1. Identify the quadratic expression.
2. Factor the quadratic expression.
3. Verify the factorization by expanding the binomials.

STEP 3

Identify the quadratic expression for problem 11:
$x^2 + 28x - 60$

STEP 4

Factor the quadratic expression $x^2 + 28x - 60$ . Look for two numbers that multiply to $-60$ and add to $28$ .
The numbers are $30$ and $-2$ .
$x^2 + 28x - 60 = (x + 30)(x - 2)$

STEP 5

Verify the factorization by expanding the binomials:
$(x + 30)(x - 2) = x^2 - 2x + 30x - 60 = x^2 + 28x - 60$
The factorization is correct.

STEP 6

Identify the quadratic expression for problem 12:
$x^2 + 7x - 30$

STEP 7

Factor the quadratic expression $x^2 + 7x - 30$ . Look for two numbers that multiply to $-30$ and add to $7$ .
The numbers are $10$ and $-3$ .
$x^2 + 7x - 30 = (x + 10)(x - 3)$

STEP 8

Verify the factorization by expanding the binomials:
$(x + 10)(x - 3) = x^2 - 3x + 10x - 30 = x^2 + 7x - 30$
The factorization is correct.
The factored forms of the quadratic expressions are: - Problem 11: $(x + 30)(x - 2)$ - Problem 12: $(x + 10)(x - 3)$

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